Mathematical Sciences: Problems in Crystal Growth and Equilibrium Shapes

数学科学：晶体生长和平衡形状问题

• 批准号: 9305929
• 负责人: Jean Taylor
• 金额: $ 11.4万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305929&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Crystal; Growth

Crystal equilibrium and growth problems involving anisotropic surface energy and/or mobility will be investigated, with and without diffusion. New theoretical frameworks for considering such problems will be developed, as will new algorithms and computer programs for computing their solutions. In particular, the crystalline approach will be further developed and applied to new problems. In this context, variational problems often become finite dimensional, and parabolic partial differential equations for surface motion become systems of ordinary differential equations. The general context for this work is geometric measure theory.

涉及各向异性表面能和/或迁移率的晶体平衡和生长问题将在有扩散和没有扩散的情况下进行研究。考虑这些问题的新理论框架将被开发出来，新的算法和计算这些问题的解决方案的计算机程序也将被开发出来。特别是，晶体方法将进一步发展和应用于新的问题。在这种情况下，变分问题往往变成有限维的，而表面运动的抛物型偏微分方程变成了常微分方程系统。这项工作的一般背景是几何测量理论。